The generator matrix

1 0 0 0 1 1 1 0 X 1 1 1 1 X 0 0 1 1 0 X 1 1 1 X X 1 X 0 1 1 1 1 X X 1 1 X 0 1
0 1 0 0 0 0 X X 1 1 1 1 X+1 1 1 X 0 1 1 1 0 X X+1 0 1 X+1 X 1 X 0 X+1 X 1 1 1 1 X 0 0
0 0 1 0 0 1 1 1 0 1 X+1 X X X+1 1 0 X+1 1 X X+1 X X+1 0 1 X 0 1 X+1 X 1 X+1 X 0 0 0 X X 1 X+1
0 0 0 1 1 X 1 X+1 1 X+1 X 0 X+1 0 1 1 0 X+1 0 X X X 1 X+1 X X 0 X+1 1 1 0 X+1 X 0 0 X+1 1 X 1
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X 0 X X 0 X X 0 X 0 X 0 X 0 X 0

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+29x^34+64x^35+65x^36+74x^37+58x^38+36x^39+35x^40+36x^41+22x^42+10x^43+21x^44+10x^45+10x^46+16x^47+4x^48+8x^49+9x^50+2x^51+2x^52

The gray image is a linear code over GF(2) with n=78, k=9 and d=34.
This code was found by Heurico 1.10 in 0 seconds.